黎曼流形中运动群不变量

The Invariant of the Group of Motions in Riemann Manifold

黎曼流形运动群的研究是微分几何中一个重要问题。构造了黎曼流形中亏数为2的一个运动群,进而对黎曼流形度规运动群、共形运动群以及亏数为2的运动群的黎曼不变量进行了刻划。证明上述3个运动群之间存在着某种所谓“自相关性”。给出黎曼空间中共形运动群在共形于黎曼空间的空间中变为度规运动群的一个有趣的例子。

The research of Rimann manifold' s the group of motions is an important question of the differential geometry. The article strac-tures a group of motions about the defective number 2 in Riemann manifold. It portraies Riemann' s invariant in Riemann' s manifold about the group of motions of the gauge, conformal and defective number being 2. We prove the three groups of motions above having the invariant. The guality of self- correlation is being in them besides. The articl shows an interesting example that the conformal group of motions in Riemann Space becomes the gauge group of motions in conformal space.